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EXPERIMENTAL
Errata Exist
Internet Engineering Task Force (IETF)                            R. PanRequest for Comments: 8033                                  P. NatarajanCategory: Experimental                                     Cisco SystemsISSN: 2070-1721                                                 F. Baker                                                            Unaffiliated                                                                G. White                                                               CableLabs                                                           February 2017Proportional Integral Controller Enhanced (PIE):A Lightweight Control Scheme to Address the Bufferbloat ProblemAbstract   Bufferbloat is a phenomenon in which excess buffers in the network   cause high latency and latency variation.  As more and more   interactive applications (e.g., voice over IP, real-time video   streaming, and financial transactions) run in the Internet, high   latency and latency variation degrade application performance.  There   is a pressing need to design intelligent queue management schemes   that can control latency and latency variation, and hence provide   desirable quality of service to users.   This document presents a lightweight active queue management design   called "PIE" (Proportional Integral controller Enhanced) that can   effectively control the average queuing latency to a target value.   Simulation results, theoretical analysis, and Linux testbed results   have shown that PIE can ensure low latency and achieve high link   utilization under various congestion situations.  The design does not   require per-packet timestamps, so it incurs very little overhead and   is simple enough to implement in both hardware and software.Pan, et al.                   Experimental                      [Page 1]

RFC 8033                           PIE                     February 2017Status of This Memo   This document is not an Internet Standards Track specification; it is   published for examination, experimental implementation, and   evaluation.   This document defines an Experimental Protocol for the Internet   community.  This document is a product of the Internet Engineering   Task Force (IETF).  It represents the consensus of the IETF   community.  It has received public review and has been approved for   publication by the Internet Engineering Steering Group (IESG).  Not   all documents approved by the IESG are a candidate for any level of   Internet Standard; seeSection 2 of RFC 7841.   Information about the current status of this document, any errata,   and how to provide feedback on it may be obtained athttp://www.rfc-editor.org/info/rfc8033.Copyright Notice   Copyright (c) 2017 IETF Trust and the persons identified as the   document authors.  All rights reserved.   This document is subject toBCP 78 and the IETF Trust's Legal   Provisions Relating to IETF Documents   (http://trustee.ietf.org/license-info) in effect on the date of   publication of this document.  Please review these documents   carefully, as they describe your rights and restrictions with respect   to this document.  Code Components extracted from this document must   include Simplified BSD License text as described in Section 4.e of   the Trust Legal Provisions and are provided without warranty as   described in the Simplified BSD License.Pan, et al.                   Experimental                      [Page 2]

RFC 8033                           PIE                     February 2017Table of Contents1. Introduction ....................................................32. Terminology .....................................................53. Design Goals ....................................................54. The Basic PIE Scheme ............................................64.1. Random Dropping ............................................74.2. Drop Probability Calculation ...............................74.3. Latency Calculation ........................................94.4. Burst Tolerance ...........................................105. Optional Design Elements of PIE ................................115.1. ECN Support ...............................................115.2. Dequeue Rate Estimation ...................................115.3. Setting PIE Active and Inactive ...........................135.4. Derandomization ...........................................145.5. Cap Drop Adjustment .......................................156. Implementation Cost ............................................157. Scope of Experimentation .......................................178. Incremental Deployment .........................................179. Security Considerations ........................................1810. References ....................................................1810.1. Normative References .....................................1810.2. Informative References ...................................18Appendix A. The Basic PIE Pseudocode ..............................21Appendix B. Pseudocode for PIE with Optional Enhancement ..........24   Contributors ......................................................29   Authors' Addresses ................................................301.  Introduction   The explosion of smart phones, tablets, and video traffic in the   Internet brings about a unique set of challenges for congestion   control.  To avoid packet drops, many service providers or   data-center operators require vendors to put in as much buffer as   possible.  Because of the rapid decrease in memory chip prices, these   requests are easily accommodated to keep customers happy.  While this   solution succeeds in assuring low packet loss and high TCP   throughput, it suffers from a major downside.  TCP continuously   increases its sending rate and causes network buffers to fill up.   TCP cuts its rate only when it receives a packet drop or mark that is   interpreted as a congestion signal.  However, drops and marks usually   occur when network buffers are full or almost full.  As a result,   excess buffers, initially designed to avoid packet drops, would lead   to highly elevated queuing latency and latency variation.  Designing   a queue management scheme is a delicate balancing act: it not only   should allow short-term bursts to smoothly pass but also should   control the average latency in the presence of long-running greedy   flows.Pan, et al.                   Experimental                      [Page 3]

RFC 8033                           PIE                     February 2017   Active Queue Management (AQM) schemes could potentially solve the   aforementioned problem.  AQM schemes, such as Random Early Detection   (RED) [RED] as suggested in [RFC2309] (which is now obsoleted by   [RFC7567]), have been around for well over a decade.  RED is   implemented in a wide variety of network devices, both in hardware   and software.  Unfortunately, due to the fact that RED needs careful   tuning of its parameters for various network conditions, most network   operators don't turn RED on.  In addition, RED is designed to control   the queue length, which would affect latency implicitly.  It does not   control latency directly.  Hence, the Internet today still lacks an   effective design that can control buffer latency to improve the   quality of experience to latency-sensitive applications.  The more   recently publishedRFC 7567 calls for new methods of controlling   network latency.   New algorithms are beginning to emerge to control queuing latency   directly to address the bufferbloat problem [CoDel].  Along these   lines, Proportional Integral controller Enhanced (PIE) also aims to   keep the benefits of RED, including easy implementation and   scalability to high speeds.  Similar to RED, PIE randomly drops an   incoming packet at the onset of congestion.  Congestion detection,   however, is based on the queuing latency instead of the queue length   (as with RED).  Furthermore, PIE also uses the derivative (rate of   change) of the queuing latency to help determine congestion levels   and an appropriate response.  The design parameters of PIE are chosen   via control theory stability analysis.  While these parameters can be   fixed to work in various traffic conditions, they could be made   self-tuning to optimize system performance.   Separately, it is assumed that any latency-based AQM scheme would be   applied over a Fair Queuing (FQ) structure or one of its approximate   designs, Flow Queuing or Class-Based Queuing (CBQ).  FQ is one of the   most studied scheduling algorithms since it was first proposed in   1985 [RFC970].  CBQ has been a standard feature in most network   devices today [CBQ].  Any AQM scheme that is built on top of FQ or   CBQ could benefit from these advantages.  Furthermore, these   advantages, such as per-flow or per-class fairness, are orthogonal to   the AQM design whose primary goal is to control latency for a given   queue.  For flows that are classified into the same class and put   into the same queue, one needs to ensure that their latency is better   controlled and that their fairness is not worse than those under the   standard DropTail or RED design.  More details about the relationship   between FQ and AQM can be found in [RFC7806].   In October 2013, CableLabs' Data-Over-Cable Service Interface   Specification 3.1 (DOCSIS 3.1) specification [DOCSIS_3.1] mandated   that cable modems implement a specific variant of the PIE design as   the active queue management algorithm.  In addition to cable-specificPan, et al.                   Experimental                      [Page 4]

RFC 8033                           PIE                     February 2017   improvements, the PIE design in DOCSIS 3.1 [RFC8034] has improved the   original design in several areas, including derandomization of coin   tosses and enhanced burst protection.   This document describes the design of PIE and separates it into basic   elements and optional components that may be implemented to enhance   the performance of PIE.2.  Terminology   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this   document are to be interpreted as described inRFC 2119 [RFC2119].3.  Design Goals   A queue management framework is designed to improve the performance   of interactive and latency-sensitive applications.  It should follow   the general guidelines set by the AQM working group document "IETF   Recommendations Regarding Active Queue Management" [RFC7567].  More   specifically, the PIE design has the following basic criteria.   *  First, queuing latency, instead of queue length, is controlled.      Queue sizes change with queue draining rates and various flows'      round-trip times.  Latency bloat is the real issue that needs to      be addressed, as it impairs real-time applications.  If latency      can be controlled, bufferbloat is not an issue.  In fact, once      latency is under control, it frees up buffers for sporadic bursts.   *  Secondly, PIE aims to attain high link utilization.  The goal of      low latency shall be achieved without suffering link      underutilization or losing network efficiency.  An early      congestion signal could cause TCP to back off and avoid queue      buildup.  On the other hand, however, TCP's rate reduction could      result in link underutilization.  There is a delicate balance      between achieving high link utilization and low latency.   *  Furthermore, the scheme should be simple to implement and easily      scalable in both hardware and software.  PIE strives to maintain      design simplicity similar to that of RED, which has been      implemented in a wide variety of network devices.   *  Finally, the scheme should ensure system stability for various      network topologies and scale well across an arbitrary number of      streams.  Design parameters shall be set automatically.  Users      only need to set performance-related parameters such as target      queue latency, not design parameters.Pan, et al.                   Experimental                      [Page 5]

RFC 8033                           PIE                     February 2017   In the following text, the design of PIE and its operation are   described in detail.4.  The Basic PIE Scheme   As illustrated in Figure 1, PIE is comprised of three simple basic   components: a) random dropping at enqueuing, b) periodic drop   probability updates, and c) latency calculation.  When a packet   arrives, a random decision is made regarding whether to drop the   packet.  The drop probability is updated periodically based on how   far the current latency is away from the target value and whether the   queuing latency is currently trending up or down.  The queuing   latency can be obtained using direct measurements or using   estimations calculated from the queue length and the dequeue rate.   The detailed definition of parameters can be found inAppendix A of   this document ("The Basic PIE Pseudocode").  Any state variables that   PIE maintains are noted using "PIE->".  For a full description of the   algorithm, one can refer to the full paper [HPSR-PIE].         Random Drop              /               --------------      -------/  -------------->    | | | | | -------------->             /|\                   | | | | |              |               --------------              |             Queue Buffer   \              |                     |       \              |                     |Queue   \              |                     |Length   \              |                     |          \              |                    \|/         \/              |          -----------------    -------------------              |          |     Drop      |    |                 |              -----<-----|  Probability  |<---| Latency         |                         |  Calculation  |    | Calculation     |                         -----------------    -------------------                        Figure 1: The PIE StructurePan, et al.                   Experimental                      [Page 6]

RFC 8033                           PIE                     February 20174.1.  Random Dropping   PIE randomly drops a packet upon its arrival to a queue according to   a drop probability, PIE->drop_prob_, that is obtained from the   drop-probability-calculation component.  The random drop is triggered   by a packet's arrival before enqueuing into a queue.   *  Upon a packet enqueue:      randomly drop the packet with a probability of PIE->drop_prob_.   To ensure that PIE is "work conserving", we bypass the random drop if   the latency sample, PIE->qdelay_old_, is smaller than half of the   target latency value (QDELAY_REF) when the drop probability is not   too high (i.e., PIE->drop_prob_ < 0.2), or if the queue has less than   a couple of packets.   *  Upon a packet enqueue, PIE does the following:      //Safeguard PIE to be work conserving      if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 0.2)            || (queue_.byte_length() <= 2 * MEAN_PKTSIZE) )                return ENQUE;      else         randomly drop the packet with a probability of         PIE->drop_prob_.   PIE optionally supports Explicit Congestion Notification (ECN); seeSection 5.1.4.2.  Drop Probability Calculation   The PIE algorithm periodically updates the drop probability based on   the latency samples -- not only the current latency sample but also   whether the latency is trending up or down.  This is the classical   Proportional Integral (PI) controller method, which is known for   eliminating steady-state errors.  This type of controller has been   studied before for controlling the queue length [PI] [QCN].  PIE   adopts the PI controller for controlling latency.  The algorithm also   auto-adjusts the control parameters based on how heavy the congestion   is, which is reflected in the current drop probability.  Note that   the current drop probability is a direct measure of the current   congestion level; there is no need to measure the arrival rate and   dequeue rate mismatches.   When a congestion period ends, we might be left with a high drop   probability with light packet arrivals.  Hence, the PIE algorithm   includes a mechanism by which the drop probability decaysPan, et al.                   Experimental                      [Page 7]

RFC 8033                           PIE                     February 2017   exponentially (rather than linearly) when the system is not   congested.  This would help the drop probability converge to 0 more   quickly, while the PI controller ensures that it would eventually   reach zero.  The decay parameter of 2% gives us a time constant   around 50 * T_UPDATE.   Specifically, the PIE algorithm periodically adjusts the drop   probability every T_UPDATE interval:   *  calculate drop probability PIE->drop_prob_, and autotune it as      follows:         p = alpha * (current_qdelay - QDELAY_REF) +                beta * (current_qdelay - PIE->qdelay_old_);         if (PIE->drop_prob_ < 0.000001) {             p /= 2048;         } else if (PIE->drop_prob_ < 0.00001) {             p /= 512;         } else if (PIE->drop_prob_ < 0.0001) {             p /= 128;         } else if (PIE->drop_prob_ < 0.001) {             p /= 32;         } else if (PIE->drop_prob_ < 0.01) {             p /= 8;         } else if (PIE->drop_prob_ < 0.1) {             p /= 2;         } else {             p = p;         }         PIE->drop_prob_ += p;   *  decay the drop probability exponentially:         if (current_qdelay == 0 && PIE->qdelay_old_ == 0) {             PIE->drop_prob_ = PIE->drop_prob_ * 0.98;                                                 //1 - 1/64 is                                                 //sufficient         }   *  bound the drop probability:         if (PIE->drop_prob_ < 0)                  PIE->drop_prob_ = 0.0         if (PIE->drop_prob_ > 1)                  PIE->drop_prob_ = 1.0Pan, et al.                   Experimental                      [Page 8]

RFC 8033                           PIE                     February 2017   *  store the current latency value:         PIE->qdelay_old_ = current_qdelay.   The update interval, T_UPDATE, is defaulted to be 15 milliseconds.   It MAY be reduced on high-speed links in order to provide smoother   response.  The target latency value, QDELAY_REF, SHOULD be set to 15   milliseconds.  The variables current_qdelay and PIE->qdelay_old_   represent the current and previous samples of the queuing latency,   which are calculated by the "latency calculation" component (seeSection 4.3).  The variable current_qdelay is actually a temporary   variable, while PIE->qdelay_old_ is a state variable that PIE keeps.   The drop probability is a value between 0 and 1.  However,   implementations can certainly use integers.   The controller parameters, alpha and beta (expressed in Hz), are   designed using feedback loop analysis, where TCP's behaviors are   modeled using the results from well-studied prior art [TCP-Models].   Note that the above adjustment of 'p' effectively scales the alpha   and beta parameters based on the current congestion level indicated   by the drop probability.   The theoretical analysis of PIE can be found in [HPSR-PIE].  As a   rule of thumb, to keep the same feedback loop dynamics, if we cut   T_UPDATE in half, we should also cut alpha by half and increase beta   by alpha/4.  If the target latency is reduced, e.g., for data-center   use, the values of alpha and beta should be increased by the same   order of magnitude by which the target latency is reduced.  For   example, if QDELAY_REF is reduced and changed from 15 milliseconds to   150 microseconds -- a reduction of two orders of magnitude -- then   alpha and beta values should be increased to alpha * 100 and   beta * 100.4.3.  Latency Calculation   The PIE algorithm uses latency to calculate drop probability in one   of two ways:   *  It estimates the current queuing latency using Little's law (seeSection 5.2 for details):         current_qdelay = queue_.byte_length()/dequeue_rate;   *  It may use other techniques for calculating queuing latency, e.g.,      time-stamp the packets at enqueue, and use the timestamps to      calculate latency during dequeue.Pan, et al.                   Experimental                      [Page 9]

RFC 8033                           PIE                     February 20174.4.  Burst Tolerance   PIE does not penalize short-term packet bursts as suggested in   [RFC7567].  PIE allows bursts of traffic that create finite-duration   events in which current queuing latency exceeds QDELAY_REF without   triggering packet drops.  This document introduces a parameter called   "MAX_BURST"; MAX_BURST defines the burst duration that will be   protected.  By default, the parameter SHOULD be set to 150   milliseconds.  For simplicity, the PIE algorithm MAY effectively   round MAX_BURST up to an integer multiple of T_UPDATE.   To implement the burst tolerance function, two basic components of   PIE are involved: "random dropping" and "drop probability   calculation".  The PIE algorithm does the following:   *  In the "random dropping" block and upon packet arrival, PIE checks      the following:      Upon a packet enqueue:         if PIE->burst_allowance_ > 0            enqueue packet;         else            randomly drop a packet with a probability of            PIE->drop_prob_.         if (PIE->drop_prob_ == 0 and current_qdelay < QDELAY_REF/2 and             PIE->qdelay_old_ < QDELAY_REF/2)             PIE->burst_allowance_ = MAX_BURST;   *  In the "drop probability calculation" block, PIE additionally      calculates:      PIE->burst_allowance_ = max(0,PIE->burst_allowance_ - T_UPDATE);   The burst allowance, noted by PIE->burst_allowance_, is initialized   to MAX_BURST.  As long as PIE->burst_allowance_ is above zero, an   incoming packet will be enqueued, bypassing the random drop process.   During each update instance, the value of PIE->burst_allowance_ is   decremented by the update period, T_UPDATE, and is bottomed at 0.   When the congestion goes away -- defined here as PIE->drop_prob_   equals 0 and both the current and previous samples of estimated   latency are less than half of QDELAY_REF -- PIE->burst_allowance_ is   reset to MAX_BURST.Pan, et al.                   Experimental                     [Page 10]

RFC 8033                           PIE                     February 20175.  Optional Design Elements of PIE   There are several enhancements that are added to further augment the   performance of the basic algorithm.  For purposes of clarity, they   are included in this section.5.1.  ECN Support   PIE MAY support ECN by marking (rather than dropping) ECN-capable   packets [ECN].  This document introduces an additional threshold   called "mark_ecnth", which acts as a safeguard: if the calculated   drop probability exceeds mark_ecnth, PIE reverts to packet-dropping   for ECN-capable packets.  The variable mark_ecnth SHOULD be set to   0.1 (10%).   *  To support ECN, the "random drop with a probability of      PIE->drop_prob_" function in the "random dropping" block is      changed to the following:      *  Upon a packet enqueue:         if rand() < PIE->drop_prob_:          if PIE->drop_prob_ < mark_ecnth && ecn_capable_packet == TRUE:             mark packet;          else             drop packet;5.2.  Dequeue Rate Estimation   Using timestamps, a latency sample can only be obtained when a packet   reaches the head of a queue.  When a quick response time is desired   or a direct latency sample is not available, one may obtain latency   through measuring the dequeue rate.  The draining rate of a queue in   the network often varies either because other queues are sharing the   same link or because the link capacity fluctuates.  Rate fluctuation   is particularly common in wireless networks.  One may measure   directly at the dequeue operation.  Short, non-persistent bursts of   packets result in empty queues from time to time; this would make the   measurement less accurate.  PIE only measures latency when there is   sufficient data in the buffer, i.e., when the queue length is over aPan, et al.                   Experimental                     [Page 11]

RFC 8033                           PIE                     February 2017   certain threshold (DQ_THRESHOLD).  PIE measures how long it takes to   drain DQ_THRESHOLD packets.  More specifically, the rate estimation   can be implemented as follows:      current_qdelay = queue_.byte_length() *                       PIE->avg_dq_time_/DQ_THRESHOLD;   *  Upon a packet dequeue:      if PIE->in_measurement_ == FALSE and queue.byte_length() >=      DQ_THRESHOLD:         PIE->in_measurement_ = TRUE;         PIE->measurement_start_ = now;         PIE->dq_count_ = 0;      if PIE->in_measurement_ == TRUE:         PIE->dq_count_ = PIE->dq_count_ + deque_pkt_size;         if PIE->dq_count_ >= DQ_THRESHOLD then            weight = DQ_THRESHOLD/2^16            PIE->avg_dq_time_ = (now - PIE->measurement_start_) *                                weight + PIE->avg_dq_time_ *                                (1 - weight);            PIE->dq_count_ = 0;            PIE->measurement_start_ = now         else            PIE->in_measurement_ = FALSE;   The parameter PIE->dq_count_ represents the number of bytes departed   since the last measurement.  Once PIE->dq_count_ is over   DQ_THRESHOLD, a measurement sample is obtained.  It is recommended   that the threshold be set to 16 KB, assuming a typical packet size of   around 1 KB or 1.5 KB.  This threshold would allow sufficient data to   obtain an average draining rate but would also be fast enough (< 64   KB) to reflect sudden changes in the draining rate.  If DQ_THRESHOLD   is smaller than 64 KB, a small weight is used to smooth out the   dequeue time and obtain PIE->avg_dq_time_.  The dequeue rate is   simply DQ_THRESHOLD divided by PIE->avg_dq_time_.  This threshold is   not crucial for the system's stability.  Please note that the update   interval for calculating the drop probability is different from the   rate measurement cycle.  The drop probability calculation is done   periodically perSection 4.2, and it is done even when the algorithm   is not in a measurement cycle; in this case, the previously latched   value of PIE->avg_dq_time_ is used.Pan, et al.                   Experimental                     [Page 12]

RFC 8033                           PIE                     February 2017            Random Drop                /                     --------------        -------/  -------------------->    | | | | | -------------->               /|\             |           | | | | |                |              |      --------------                |              |       Queue Buffer                |              |             |                |              |             |Queue                |              |             |Length                |              |             |                |             \|/           \|/                |          ------------------------------                |          |     Dequeue Rate           |                -----<-----|  & Drop Probability        |                           |        Calculation         |                           ------------------------------                 Figure 2: The Enqueue-Based PIE Structure   In some platforms, enqueuing and dequeuing functions belong to   different modules that are independent of each other.  In such   situations, a pure enqueue-based design can be developed.  An   enqueue-based design is depicted in Figure 2.  The dequeue rate is   deduced from the number of packets enqueued and the queue length.   The design is based on the following key observation: over a certain   time interval, the number of dequeued packets = the number of   enqueued packets minus the number of remaining packets in the queue.   In this design, everything can be triggered by packet arrival,   including the background update process.  The design complexity here   is similar to the original design.5.3.  Setting PIE Active and Inactive   Traffic naturally fluctuates in a network.  It would be preferable   not to unnecessarily drop packets due to a spurious uptick in queuing   latency.  PIE has an optional feature of automatically becoming   active/inactive.  To implement this feature, PIE may choose to only   become active (from inactive) when the buffer occupancy is over a   certain threshold, which may be set to 1/3 of the tail drop   threshold.  PIE becomes inactive when congestion ends; i.e., when the   drop probability reaches 0, current and previous latency samples are   all below half of QDELAY_REF.   Ideally, PIE should become active/inactive based on latency.   However, calculating latency when PIE is inactive would introduce   unnecessary packet-processing overhead.  Weighing the trade-offs,   we decided to compare against the tail drop threshold to keep things   simple.Pan, et al.                   Experimental                     [Page 13]

RFC 8033                           PIE                     February 2017   When PIE optionally becomes active/inactive, the burst protection   logic described inSection 4.4 is modified as follows:   *  "Random dropping" block: PIE adds the following:      Upon packet arrival:      if PIE->active_ == FALSE && queue_length >= TAIL_DROP/3:         PIE->active_ = TRUE;         PIE->burst_allowance_ = MAX_BURST;      if PIE->burst_allowance_ > 0         enqueue packet;      else         randomly drop a packet with a probability of         PIE->drop_prob_.      if (PIE->drop_prob_ == 0 and current_qdelay < QDELAY_REF/2 and          PIE->qdelay_old_ < QDELAY_REF/2)          PIE->active_ = FALSE;          PIE->burst_allowance_ = MAX_BURST;   *  "Drop probability calculation" block: PIE does the following:      if PIE->active_ == TRUE:         PIE->burst_allowance_ =            max(0,PIE->burst_allowance_ - T_UPDATE);5.4.  Derandomization   Although PIE adopts random dropping to achieve latency control,   independent coin tosses could introduce outlier situations where   packets are dropped too close to each other or too far from each   other.  This would cause the real drop percentage to temporarily   deviate from the intended value PIE->drop_prob_.  In certain   scenarios, such as a small number of simultaneous TCP flows, these   deviations can cause significant deviations in link utilization and   queuing latency.  PIE may use a derandomization mechanism to avoid   such situations.  A parameter called "PIE->accu_prob_" is reset to 0   after a drop.  Upon packet arrival, PIE->accu_prob_ is incremented by   the amount of drop probability, PIE->drop_prob_.  If PIE->accu_prob_   is less than a low threshold, e.g., 0.85, the arriving packet is   enqueued; on the other hand, if PIE->accu_prob_ is more than a high   threshold, e.g., 8.5, and the queue is congested, the arrival packet   is forced to be dropped.  A packet is only randomly dropped if   PIE->accu_prob_ falls between the two thresholds.  Since   PIE->accu_prob_ is reset to 0 after a drop, another drop will not   happen until 0.85/PIE->drop_prob_ packets later.  This avoids packets   being dropped too close to each other.  In the other extreme casePan, et al.                   Experimental                     [Page 14]

RFC 8033                           PIE                     February 2017   where 8.5/PIE->drop_prob_ packets have been enqueued without   incurring a drop, PIE would force a drop in order to prevent the   drops from being spaced too far apart.  Further analysis can be found   in [RFC8034].5.5.  Cap Drop Adjustment   In the case of a single TCP flow, during the slow-start phase the   queue could quickly increase, which could result in a very rapid   increase in drop probability.  In order to prevent an excessive   ramp-up that could negatively impact the throughput in this scenario,   PIE can cap the maximum drop probability increase in each step.   *  "Drop probability calculation" block: PIE adds the following:      if (PIE->drop_prob_ >= 0.1 && p > 0.02) {          p = 0.02;      }6.  Implementation Cost   PIE can be applied to existing hardware or software solutions.  There   are three steps involved in PIE, as discussed inSection 4.  Their   complexities are examined below.   Upon packet arrival, the algorithm simply drops a packet randomly,   based on the drop probability.  This step is straightforward and   requires no packet header examination and manipulation.  If the   implementation doesn't rely on packet timestamps for calculating   latency, PIE does not require extra memory.  Furthermore, the input   side of a queue is typically under software control while the output   side of a queue is hardware based.  Hence, a drop at enqueuing can be   readily retrofitted into existing or software implementations.   The drop probability calculation is done in the background, and it   occurs every T_UPDATE interval.  Given modern high-speed links, this   period translates into once every tens, hundreds, or even thousands   of packets.  Hence, the calculation occurs at a much slower time   scale than the packet-processing time -- at least an order of   magnitude slower.  The calculation of drop probability involves   multiplications using alpha and beta.  Since PIE's control law is   robust to minor changes in alpha and beta values, an implementation   MAY choose these values to the closest multiples of 2 or 1/2 (e.g.,   alpha = 1/8, beta = 1 + 1/4) such that the multiplications can be   done using simple adds and shifts.  As no complicated functions are   required, PIE can be easily implemented in both hardware andPan, et al.                   Experimental                     [Page 15]

RFC 8033                           PIE                     February 2017   software.  The state requirement is only three variables per queue:   burst_allowance_, PIE->drop_prob_, and PIE->qdelay_old_.  Hence, the   memory overhead is small.   If one chooses to implement the departure rate estimation, PIE uses a   counter to keep track of the number of bytes departed for the current   interval.  This counter is incremented per packet departure.  Every   T_UPDATE, PIE calculates latency using the departure rate, which can   be implemented using a single multiply operation.  Note that many   network devices keep track of an interface's departure rate.  In this   case, PIE might be able to reuse this information and simply skip the   third step of the algorithm; hence, it would incur no extra cost.  If   a platform already leverages packet timestamps for other purposes,   PIE can make use of these packet timestamps for latency calculation   instead of estimating the departure rate.   Flow queuing can also be combined with PIE to provide isolation   between flows.  In this case, it is preferable to have an independent   value of drop probability per queue.  This allows each flow to   receive the most appropriate level of congestion signal and ensures   that sparse flows are protected from experiencing packet drops.   However, running the entire PIE algorithm independently on each queue   in order to calculate the drop probability may be overkill.   Furthermore, in the case where departure rate estimation is used to   predict queuing latency, it is not possible to calculate an accurate   per-queue departure rate upon which to implement the PIE drop   probability calculation.  Instead, it has been proposed [DOCSIS-AQM]   that a single implementation of the PIE drop probability calculation   based on the overall latency estimate be used, followed by a   per-queue scaling of drop probability based on the ratio of   queue depth between the queue in question and the current largest   queue.  This scaling is reasonably simple and has a couple of nice   properties:   *  If a packet is arriving to an empty queue, it is given immunity      from packet drops altogether, regardless of the state of the other      queues.   *  In the situation where only a single queue is in use, the      algorithm behaves exactly like the single-queue PIE algorithm.   In summary, PIE is simple enough to be implemented in both software   and hardware.Pan, et al.                   Experimental                     [Page 16]

RFC 8033                           PIE                     February 20177.  Scope of Experimentation   The design of the PIE algorithm is presented in this document.  The   PIE algorithm effectively controls the average queuing latency to a   target value.  The following areas can be used for further study and   experimentation:   *  Autotuning of target latency without losing utilization.   *  Autotuning for the average round-trip time of traffic.   *  The proper threshold to transition smoothly between ECN marking      and dropping.   *  The enhancements described inSection 5, which can be used in      experiments to see if they would be of more value in the real      world.  If so, they will be incorporated into the basic PIE      algorithm.   *  The PIE design, which is separated into the data path and the      control path.  The control path can be implemented in software.      Field tests of other control laws can be performed to experiment      with further improvements to PIE's performance.   Although all network nodes cannot be changed altogether to adopt   latency-based AQM schemes such as PIE, a gradual adoption would   eventually lead to end-to-end low-latency service for all   applications.8.  Incremental Deployment   From testbed experiments and large-scale simulations of PIE so far,   PIE has been shown to be effective across a diverse range of network   scenarios.  There is no indication that PIE would be harmful to   deploy.   The PIE scheme can be independently deployed and managed without a   need for interoperability between different network devices.  In   addition, any individual buffer queue can be incrementally upgraded   to PIE, as it can coexist with existing AQM schemes such as   Weighted RED (WRED).   PIE is intended to be self-configuring.  Users should not need to   configure any design parameters.  Upon installation, the two   user-configurable parameters -- QDELAY_REF and MAX_BURST -- will be   defaulted to 15 milliseconds and 150 milliseconds for non-data-center   network devices and to 15 microseconds and 150 microseconds for   data-center switches, respectively.Pan, et al.                   Experimental                     [Page 17]

RFC 8033                           PIE                     February 2017   Since the data path of the algorithm needs only a simple coin toss   and the control-path calculation happens in a much slower time scale,   we don't foresee any scaling issues associated with the algorithm as   the link speed scales up.9.  Security Considerations   This document describes PIE, an active queue management algorithm   based on implementations in different products.  The PIE algorithm   introduces no specific security exposures.10.  References10.1.  Normative References   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate              Requirement Levels",BCP 14,RFC 2119,              DOI 10.17487/RFC2119, March 1997,              <http://www.rfc-editor.org/info/rfc2119>.10.2.  Informative References   [RFC970]   Nagle, J., "On Packet Switches With Infinite Storage",RFC 970, DOI 10.17487/RFC0970, December 1985,              <http://www.rfc-editor.org/info/rfc970>.   [RFC2309]  Braden, B., Clark, D., Crowcroft, J., Davie, B., Deering,              S., Estrin, D., Floyd, S., Jacobson, V., Minshall, G.,              Partridge, C., Peterson, L., Ramakrishnan, K., Shenker,              S., Wroclawski, J., and L. Zhang, "Recommendations on              Queue Management and Congestion Avoidance in the              Internet",RFC 2309, DOI 10.17487/RFC2309, April 1998,              <http://www.rfc-editor.org/info/rfc2309>.   [RFC7567]  Baker, F., Ed., and G. Fairhurst, Ed., "IETF              Recommendations Regarding Active Queue Management",BCP 197,RFC 7567, DOI 10.17487/RFC7567, July 2015,              <http://www.rfc-editor.org/info/rfc7567>.   [RFC7806]  Baker, F. and R. Pan, "On Queuing, Marking, and Dropping",RFC 7806, DOI 10.17487/RFC7806, April 2016,              <http://www.rfc-editor.org/info/rfc7806>.Pan, et al.                   Experimental                     [Page 18]

RFC 8033                           PIE                     February 2017   [RFC8034]  White, G. and R. Pan, "Active Queue Management (AQM) Based              on Proportional Integral Controller Enhanced (PIE) for              Data-Over-Cable Service Interface Specifications (DOCSIS)              Cable Modems",RFC 8034, DOI 10.17487/RFC8034,              February 2017, <http://www.rfc-editor.org/info/rfc8034>.   [CBQ]      Cisco, "Class-Based Weighted Fair Queueing",              <http://www.cisco.com/en/US/docs/ios/12_0t/12_0t5/feature/guide/cbwfq.html>.   [CoDel]    Nichols, K. and V. Jacobson, "Controlling Queue Delay",              Communications of the ACM, Volume 55, Issue 7, pp. 42-50,              DOI 10.1145/2209249.2209264, July 2012.   [DOCSIS_3.1]              CableLabs, "MAC and Upper Layer Protocols Interface              Specification", DOCSIS 3.1, January 2017,              <https://apps.cablelabs.com/specification/CM-SP-MULPIv3.1>.   [DOCSIS-AQM]              White, G., "Active Queue Management in DOCSIS 3.x Cable              Modems", May 2014, <http://www.cablelabs.com/wp-content/uploads/2014/06/DOCSIS-AQM_May2014.pdf>.   [ECN]      Briscoe, B., Kaippallimalil, J., and P. Thaler,              "Guidelines for Adding Congestion Notification to              Protocols that Encapsulate IP", Work in Progress,draft-ietf-tsvwg-ecn-encap-guidelines-07, July 2016.   [HPSR-PIE] Pan, R., Natarajan, P., Piglione, C., Prabhu, M.S.,              Subramanian, V., Baker, F., and B. Ver Steeg, "PIE: A              lightweight control scheme to address the bufferbloat              problem", IEEE HPSR, DOI 10.1109/HPSR.2013.6602305, 2013,              <https://www.researchgate.net/publication/261134127_PIE_A_lightweight_control_scheme_to_address_the_bufferbloat_problem?origin=mail>.   [PI]       Hollot, C.V., Misra, V., Towsley, D., and W. Gong, "On              designing improved controllers for AQM routers supporting              TCP flows", INFOCOM 2001, DOI 10.1109/INFCOM.2001.916670,              April 2001.   [QCN]      IEEE, "IEEE Standard for Local and Metropolitan Area              Networks--Virtual Bridged Local Area Networks -              Amendment: 10: Congestion Notification", IEEE 802.1Qau,              <http://www.ieee802.org/1/pages/802.1au.html>.Pan, et al.                   Experimental                     [Page 19]

RFC 8033                           PIE                     February 2017   [RED]      Floyd, S. and V. Jacobson, "Random Early Detection (RED)              Gateways for Congestion Avoidance", IEEE/ACM Transactions              on Networking, Volume 1, Issue 4, DOI 10.1109/90.251892,              August 1993.   [TCP-Models]              Misra, V., Gong, W., and D. Towsley, "Fluid-based analysis              of a network of AQM routers supporting TCP flows with an              application to RED", SIGCOMM 2000, Volume 30, Issue 4,              pp. 151-160, DOI 10.1145/347057.347421, October 2000.Pan, et al.                   Experimental                     [Page 20]

RFC 8033                           PIE                     February 2017Appendix A.  The Basic PIE Pseudocode   Configurable parameters:      -  QDELAY_REF.  AQM Latency Target (default: 15 milliseconds)      -  MAX_BURST.  AQM Max Burst Allowance (default: 150 milliseconds)   Internal parameters:      -  Weights in the drop probability calculation (1/s):         alpha (default: 1/8), beta (default: 1 + 1/4)      -  T_UPDATE: a period to calculate drop probability         (default: 15 milliseconds)   Table that stores status variables (ending with "_"):      -  burst_allowance_: current burst allowance      -  drop_prob_: The current packet drop probability.  Reset to 0      -  qdelay_old_: The previous queue delay.  Reset to 0   Public/system functions:      -  queue_.  Holds the pending packets      -  drop(packet).  Drops/discards a packet      -  now().  Returns the current time      -  random().  Returns a uniform r.v. in the range 0 ~ 1      -  queue_.byte_length().  Returns current queue_ length in bytes      -  queue_.enque(packet).  Adds packet to tail of queue_      -  queue_.deque().  Returns the packet from the head of queue_      -  packet.size().  Returns size of packet      -  packet.timestamp_delay().  Returns timestamped packet latency   ============================   //Called on each packet arrival     enque(Packet packet) {          if (PIE->drop_prob_ == 0 && current_qdelay < QDELAY_REF/2              && PIE->qdelay_old_ < QDELAY_REF/2) {              PIE->burst_allowance_ = MAX_BURST;          }          if (PIE->burst_allowance_ == 0 && drop_early() == DROP) {                   drop(packet);          } else {                   queue_.enque(packet);          }     }   ============================Pan, et al.                   Experimental                     [Page 21]

RFC 8033                           PIE                     February 2017     drop_early() {         //Safeguard PIE to be work conserving         if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 0.2)               || (queue_.byte_length() <= 2 * MEAN_PKTSIZE) ) {              return ENQUE;         }         double u = random();         if (u < PIE->drop_prob_) {              return DROP;         } else {              return ENQUE;         }      }   ============================   //We choose the timestamp option of obtaining latency for clarity   //Rate estimation method can be found in the extended PIE pseudocode     deque(Packet packet) {       current_qdelay = packet.timestamp_delay();     }   ============================   //Update periodically, T_UPDATE = 15 milliseconds     calculate_drop_prob() {          //Can be implemented using integer multiply          p = alpha * (current_qdelay - QDELAY_REF) + \              beta * (current_qdelay - PIE->qdelay_old_);          if (PIE->drop_prob_ < 0.000001) {              p /= 2048;          } else if (PIE->drop_prob_ < 0.00001) {              p /= 512;          } else if (PIE->drop_prob_ < 0.0001) {              p /= 128;          } else if (PIE->drop_prob_ < 0.001) {              p /= 32;          } else if (PIE->drop_prob_ < 0.01) {              p /= 8;Pan, et al.                   Experimental                     [Page 22]

RFC 8033                           PIE                     February 2017          } else if (PIE->drop_prob_ < 0.1) {              p /= 2;          } else {              p = p;          }          PIE->drop_prob_ += p;          //Exponentially decay drop prob when congestion goes away          if (current_qdelay == 0 && PIE->qdelay_old_ == 0) {              PIE->drop_prob_ *= 0.98;           //1 - 1/64 is                                                 //sufficient          }          //Bound drop probability          if (PIE->drop_prob_ < 0)                   PIE->drop_prob_ = 0.0          if (PIE->drop_prob_ > 1)                   PIE->drop_prob_ = 1.0          PIE->qdelay_old_ = current_qdelay;          PIE->burst_allowance_ =             max(0,PIE->burst_allowance_ - T_UPDATE);       }   }Pan, et al.                   Experimental                     [Page 23]

RFC 8033                           PIE                     February 2017Appendix B.  Pseudocode for PIE with Optional Enhancement   Configurable parameters:      -  QDELAY_REF.  AQM Latency Target (default: 15 milliseconds)      -  MAX_BURST.  AQM Max Burst Allowance (default: 150 milliseconds)      -  MAX_ECNTH.  AQM Max ECN Marking Threshold (default: 10%)   Internal parameters:      -  Weights in the drop probability calculation (1/s):         alpha (default: 1/8), beta (default: 1 + 1/4)      -  DQ_THRESHOLD: (in bytes, default: 2^14 (in a power of 2) )      -  T_UPDATE: a period to calculate drop probability         (default: 15 milliseconds)      -  TAIL_DROP: the tail drop threshold (max allowed queue depth)         for the queue   Table that stores status variables (ending with "_"):      -  active_: INACTIVE/ACTIVE      -  burst_allowance_: current burst allowance      -  drop_prob_: The current packet drop probability.  Reset to 0      -  accu_prob_: Accumulated drop probability.  Reset to 0      -  qdelay_old_: The previous queue delay estimate.  Reset to 0      -  last_timestamp_: Timestamp of previous status update      -  dq_count_, measurement_start_, in_measurement_, avg_dq_time_.         Variables for measuring average dequeue rate   Public/system functions:      -  queue_.  Holds the pending packets      -  drop(packet).  Drops/discards a packet      -  mark(packet).  Marks ECN for a packet      -  now().  Returns the current time      -  random().  Returns a uniform r.v. in the range 0 ~ 1      -  queue_.byte_length().  Returns current queue_ length in bytes      -  queue_.enque(packet).  Adds packet to tail of queue_      -  queue_.deque().  Returns the packet from the head of queue_      -  packet.size().  Returns size of packet      -  packet.ecn().  Returns whether packet is ECN capable or not   ============================Pan, et al.                   Experimental                     [Page 24]

RFC 8033                           PIE                     February 2017   //Called on each packet arrival     enque(Packet packet) {          if (queue_.byte_length() + packet.size() > TAIL_DROP) {                 drop(packet);                 PIE->accu_prob_ = 0;          } else if (PIE->active_ == TRUE && drop_early() == DROP                     && PIE->burst_allowance_ == 0) {                 if (PIE->drop_prob_ < MAX_ECNTH && packet.ecn() ==                     TRUE)                       mark(packet);                 else                       drop(packet);                       PIE->accu_prob_ = 0;          } else {                 queue_.enque(packet);          }          //If the queue is over a certain threshold, turn on PIE          if (PIE->active_ == INACTIVE              && queue_.byte_length() >= TAIL_DROP/3) {               PIE->active_ = ACTIVE;               PIE->qdelay_old_ = 0;               PIE->drop_prob_ = 0;               PIE->in_measurement_ = TRUE;               PIE->dq_count_ = 0;               PIE->avg_dq_time_ = 0;               PIE->last_timestamp_ = now;               PIE->burst_allowance_ = MAX_BURST;               PIE->accu_prob_ = 0;               PIE->measurement_start_ = now;          }          //If the queue has been idle for a while, turn off PIE          //Reset counters when accessing the queue after some idle          //period if PIE was active before          if ( PIE->drop_prob_ == 0 && PIE->qdelay_old_ == 0               && current_qdelay == 0) {               PIE->active_ = INACTIVE;               PIE->in_measurement_ = FALSE;          }     }   ============================Pan, et al.                   Experimental                     [Page 25]

RFC 8033                           PIE                     February 2017     drop_early() {         //PIE is active but the queue is not congested: return ENQUE         if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 0.2)               || (queue_.byte_length() <= 2 * MEAN_PKTSIZE) ) {              return ENQUE;         }         if (PIE->drop_prob_ == 0) {                  PIE->accu_prob_ = 0;         }         //For practical reasons, drop probability can be further scaled         //according to packet size, but one needs to set a bound to         //avoid unnecessary bias         //Random drop         PIE->accu_prob_ += PIE->drop_prob_;         if (PIE->accu_prob_ < 0.85)             return ENQUE;         if (PIE->accu_prob_ >= 8.5)             return DROP;                 double u = random();         if (u < PIE->drop_prob_) {                      PIE->accu_prob_ = 0;                      return DROP;         } else {                      return ENQUE;         }      }   ============================Pan, et al.                   Experimental                     [Page 26]

RFC 8033                           PIE                     February 2017    //Update periodically, T_UPDATE = 15 milliseconds    calculate_drop_prob() {        if ( (now - PIE->last_timestamp_) >= T_UPDATE &&                PIE->active_ == ACTIVE) {          //Can be implemented using integer multiply          //DQ_THRESHOLD is power of 2 value          current_qdelay = queue_.byte_length() *          PIE->avg_dq_time_/DQ_THRESHOLD;          p = alpha * (current_qdelay - QDELAY_REF) + \              beta * (current_qdelay - PIE->qdelay_old_);          if (PIE->drop_prob_ < 0.000001) {              p /= 2048;          } else if (PIE->drop_prob_ < 0.00001) {              p /= 512;          } else if (PIE->drop_prob_ < 0.0001) {              p /= 128;          } else if (PIE->drop_prob_ < 0.001) {              p /= 32;          } else if (PIE->drop_prob_ < 0.01) {              p /= 8;          } else if (PIE->drop_prob_ < 0.1) {              p /= 2;          } else {              p = p;          }          if (PIE->drop_prob_ >= 0.1 && p > 0.02) {              p = 0.02;          }          PIE->drop_prob_ += p;          //Exponentially decay drop prob when congestion goes away          if (current_qdelay < QDELAY_REF/2 && PIE->qdelay_old_ <              QDELAY_REF/2) {                 PIE->drop_prob_ *= 0.98;        //1 - 1/64 is                                                 //sufficient          }Pan, et al.                   Experimental                     [Page 27]

RFC 8033                           PIE                     February 2017          //Bound drop probability          if (PIE->drop_prob_ < 0)                   PIE->drop_prob_ = 0          if (PIE->drop_prob_ > 1)                   PIE->drop_prob_ = 1          PIE->qdelay_old_ = current_qdelay;          PIE->last_timestamp_ = now;          PIE->burst_allowance_ = max(0,PIE->burst_allowance_ -             T_UPDATE);       }   }   ============================   //Called on each packet departure     deque(Packet packet) {        //Dequeue rate estimation        if (PIE->in_measurement_ == TRUE) {             PIE->dq_count_ = packet.size() + PIE->dq_count_;             //Start a new measurement cycle if we have enough packets             if ( PIE->dq_count_ >= DQ_THRESHOLD) {               dq_time = now - PIE->measurement_start_;               if (PIE->avg_dq_time_ == 0) {                   PIE->avg_dq_time_ = dq_time;               } else {                   weight = DQ_THRESHOLD/2^16                   PIE->avg_dq_time_ = dq_time * weight +                      PIE->avg_dq_time_ * (1 - weight);               }               PIE->in_measurement_ = FALSE;             }        }        //Start a measurement if we have enough data in the queue        if (queue_.byte_length() >= DQ_THRESHOLD &&            PIE->in_measurement_ == FALSE) {               PIE->in_measurement_ = TRUE;               PIE->measurement_start_ = now;               PIE->dq_count_ = 0;        }     }Pan, et al.                   Experimental                     [Page 28]

RFC 8033                           PIE                     February 2017Contributors   Bill Ver Steeg   Comcast Cable   Email: William_VerSteeg@comcast.com   Mythili Prabhu*   Akamai Technologies   3355 Scott Blvd.   Santa Clara, CA  95054   United States of America   Email: mythili@akamai.com   Chiara Piglione*   Broadcom Corporation   3151 Zanker Road   San Jose, CA  95134   United States of America   Email: chiara@broadcom.com   Vijay Subramanian*   PLUMgrid, Inc.   350 Oakmead Parkway   Suite 250   Sunnyvale, CA  94085   United States of America   Email: vns@plumgrid.com   * Formerly at Cisco SystemsPan, et al.                   Experimental                     [Page 29]

RFC 8033                           PIE                     February 2017Authors' Addresses   Rong Pan   Cisco Systems   3625 Cisco Way   San Jose, CA  95134   United States of America   Email: ropan@cisco.com   Preethi Natarajan   Cisco Systems   725 Alder Drive   Milpitas, CA  95035   United States of America   Email: prenatar@cisco.com   Fred Baker   Santa Barbara, CA  93117   United States of America   Email: FredBaker.IETF@gmail.com   Greg White   CableLabs   858 Coal Creek Circle   Louisville, CO  80027   United States of America   Email: g.white@cablelabs.comPan, et al.                   Experimental                     [Page 30]

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